Publications

2026

1. bioRxiv

   State-Dependent Organization of Microscale Functional Circuitry in Visual Cortex

   Rahul Biswas, Hasika Wickrama Senevirathne, Yujing Wang, and 3 more authors

   bioRxiv, 2026

   In preparation for submission to Nature Neuroscience

   Abs DOI

   Brain state modulates sensory processing across visual cortex, yet how it relates to the organization of functional circuitry at the level of individual neurons and cell types remains largely unknown. To address this, we constructed one of the largest microscale directed functional circuit maps in mouse visual cortex from calcium imaging of more than 57,000 neurons across four visual areas and five cortical layers. Using a time-aware causal inference framework, we found that intra-areal connections dominate across arousal states, consistent with experimental findings on the local bias of cortical anatomy. Among intra-areal connections, anterolateral area (AL) had the highest density, and among inter-areal connections, the AL-rostrolateral area (RL) axis formed the strongest pathway. Laminar circuit organization was dominated by layer 6 recurrence within-layer, while the most prominent between-layer pathway was layer 5-to-layer 6 in low arousal and layer 4-to-layer 5 in high arousal. Spatial extent was selectively greater for excitatory-to-inhibitory connections in high arousal, but not for excitatory-to-excitatory connections. Across 6,597 electron-microscopy reconstructions of neuron pairs, synapse count predicted functional connection strength in both arousal states, but structure-function coupling was weaker in high arousal. In stimulus-driven response prediction, neuron pairs with stronger functional connections exhibited more similar predictive performance in both states, with performance varying by layer and cell type. Overall, our findings map, at single-neuron resolution, the multi-scale organization of directed functional circuitry in mouse visual cortex across brain states.

2025

1. arXiv

   CITS: Nonparametric Statistical Causal Modeling for High-Resolution Neural Time Series

   Rahul Biswas, SuryaNarayana Sripada, Somabha Mukherjee, and 1 more author

   2025

   Under review at Nature Communications

   Abs DOI

   Identifying causal interactions in complex dynamical systems is a fundamental challenge across the computational sciences. Existing functional connectivity methods capture correlations but not causation. While addressing directionality, popular causal inference tools such as Granger causality and the Peter-Clark algorithm rely on restrictive assumptions that limit their applicability to high-resolution time-series data, such as the large-scale recordings now standard in neuroscience. Here, we introduce CITS (Causal Inference in Time Series), a nonparametric framework for inferring statistically causal structure from multivariate time series. CITS models dynamics using a structural causal model of arbitrary Markov order and statistical tests for lagged conditional independence. We prove consistency under mild assumptions and demonstrate superior accuracy over state-of-the-art baselines across simulated linear, nonlinear, and recurrent neural network benchmarks. Applying CITS to large-scale neuronal recordings from the mouse visual cortex, thalamus, and hippocampus, we uncover stimulus-specific causal pathways and inter-regional hierarchies that align with known anatomy while revealing new functional insights. We further highlight CITS ability in accurately identifying conditional dependencies within small inferred neuronal motifs. These results establish CITS as a theoretically grounded and empirically validated method for discovering interpretable statistically causal networks in neural time series. Beyond neuroscience, the framework is broadly applicable to causal discovery in complex temporal systems across domains.

2. J. Dementia AD

   Alterations in Causal Functional Brain Networks in Alzheimer’s Disease: A Resting-State fMRI Study

   Rahul Biswas and SuryaNarayana Sripada

   Journal of Dementia and Alzheimer’s Disease, 2025

   Abs DOI

   Background: Alterations in brain functional connectivity (FC) precede clinical symptoms of Alzheimer’s disease (AD) by decades, presenting opportunities for early diagnosis. However, conventional FC analyses measure correlations between brain regions and do not provide insights into directional, causal interactions. Causal functional connectivity (CFC), which infers directed interactions between regions, addresses this limitation. This study aims to identify disrupted CFC networks in AD compared to cognitively normal (CN) individuals. Methods: The recently developed Time-aware PC (TPC) algorithm was employed to infer directed CFC from functional magnetic resonance imaging (fMRI) data. These results were compared with traditional correlation-based FC obtained via sparse partial correlation. Network-based Statistics (NBS) for directed networks was used to identify altered CFC sub-networks, with corrections for multiple comparisons applied at the 5% significance level. Results: Key causal networks, including the inferior frontal gyrus, superior temporal gyrus, middle temporal gyrus, and cerebellum, showed significantly reduced strength in AD compared to CN (p = 0.0299; NBS corrected). Conclusions: This study demonstrates the utility of CFC analysis in uncovering network-level disruptions in AD. The identified disrupted networks align with published medical literature and provide a framework for future studies with larger datasets.

2024

1. Stat. Comput.

   Consistent Causal Inference from Time Series with PC Algorithm and its Time-Aware Extension

   Rahul Biswas and Somabha Mukherjee

   Statistics and Computing, 2024

   Abs DOI

   The estimator of a causal directed acyclic graph (DAG) with the PC algorithm is known to be consistent based on independent and identically distributed samples. In this paper, we consider the scenario when the multivariate samples are identically distributed but not independent. A common example is a stationary multivariate time series. We show that under a standard set of assumptions on the underlying time series involving rho-mixing, the PC algorithm is consistent in this dependent sample scenario. Further, we show that for the popular time series models such as vector auto-regressive moving average and linear processes, consistency of the PC algorithm holds. We also prove the consistency for the Time-Aware PC algorithm, a recent adaptation of the PC algorithm for the time series scenario. Our findings are supported by simulations and benchmark real data analyses provided towards the end of the paper.

2. J. Multivar. Anal.

   Tensor Recovery in High-Dimensional Ising Models

   Tianyu Liu, Somabha Mukherjee, and Rahul Biswas

   Journal of Multivariate Analysis, 2024

   Abs DOI

   The k-tensor Ising model is an exponential family on a p-dimensional binary hypercube for modeling dependent binary data, where the sufficient statistic consists of all k-fold products of the observations, and the parameter is an unknown k-fold tensor, designed to capture higher-order interactions between the binary variables. In this paper, we describe an approach based on a penalization technique that helps us recover the signed support of the tensor parameter with high probability, assuming that no entry of the true tensor is too close to zero. The method is based on an l1-regularized node-wise logistic regression, that recovers the signed neighborhood of each node with high probability. Our analysis is carried out in the high-dimensional regime, that allows the dimension p of the Ising model, as well as the interaction factor k to potentially grow to infinity with the sample size n. Our results are validated in two simulation settings, and applied on a real neurobiological dataset consisting of multi-array electro-physiological recordings from the mouse visual cortex, to model higher-order interactions between the brain regions.

2023

1. Front. Comp. Neuro.

   Causal Functional Connectivity in Alzheimer’s Disease Computed from Time Series fMRI Data

   Rahul Biswas and SuryaNarayana Sripada

   Frontiers in Computational Neuroscience, 2023

   Abs DOI

   Functional connectivity between brain regions is known to be altered in Alzheimer’s disease and promises to be a biomarker for early diagnosis. Several approaches for functional connectivity obtain an undirected network representing stochastic associations (correlations) between brain regions. However, association does not necessarily imply causation. In contrast, Causal Functional Connectivity (CFC) is more informative, providing a directed network representing causal relationships between brain regions. In this paper, we obtained the causal functional connectome for the whole brain from resting-state functional magnetic resonance imaging (rs-fMRI) recordings of subjects from three clinical groups: cognitively normal, mild cognitive impairment, and Alzheimer’s disease. We applied the recently developed Time-aware PC (TPC) algorithm to infer the causal functional connectome for the whole brain. TPC supports model-free estimation of whole brain CFC based on directed graphical modeling in a time series setting. We compared the CFC outcome of TPC with that of other related approaches in the literature. Then, we used the CFC outcomes of TPC and performed an exploratory analysis of the difference in strengths of CFC edges between Alzheimer’s and cognitively normal groups, based on edge-wise p-values obtained by Welch’s t-test. The brain regions thus identified are found to be in agreement with literature on brain regions impacted by Alzheimer’s disease, published by researchers from clinical/medical institutions.

2. BMC Med. Res. Meth.

   Functional Data Analysis to Characterize Disease Patterns in Frequent Longitudinal Data: Application to Bacterial Vaginal Microbiota Patterns Using Weekly Nugent Scores and Identification of Pattern-Specific Risk Factors

   Rahul Biswas, Marie Thoma, and Xiangrong Kong

   BMC Medical Research Methodology, 2023

   Abs DOI

   Background: Technology advancement has allowed more frequent monitoring of biomarkers. The resulting data structure entails more frequent follow-ups compared to traditional longitudinal studies where the number of follow-up is often small. Such data allow explorations of the role of intra-person variability in understanding disease etiology and characterizing disease processes. Methods: We use a fully data-driven approach to characterize the longitudinal patterns of vaginal microbiota by considering the densely sampled Nugent scores to be random functions over time and performing dimension reduction by functional principal components. Extending a current functional data clustering method, we use a hierarchical functional clustering framework considering multiple data features to help identify clinically meaningful patterns of vaginal microbiota fluctuations. Additionally, multinomial logistic regression was used to identify risk factors for each vaginal microbiota pattern. Results: Using weekly Nugent scores over 2 years of 211 sexually active and post-menarcheal women in Rakai, four patterns of vaginal microbiota variation were identified. Higher Nugent score at the start of an interval, younger age group of less than 20 years, unprotected source for bathing water, a woman’s partner’s being not circumcised, and use of injectable/Norplant hormonal contraceptives were associated with higher odds of persistent BV. Conclusion: The hierarchical functional data clustering method can be used for fully data-driven unsupervised clustering of densely sampled longitudinal data to identify clinically informative clusters and risk factors associated with each cluster.

2022

1. PLoS Comput. Biol.

   Statistical Perspective on Functional and Causal Neural Connectomics: The Time-Aware PC Algorithm

   Rahul Biswas and Eli Shlizerman

   PLOS Computational Biology, 2022

   Abs DOI

   The representation of the flow of information between neurons in the brain based on their activity is termed the causal functional connectome. Such representation incorporates the dynamic nature of neuronal activity and causal interactions between them. In contrast to connectome, the causal functional connectome is not directly observed and needs to be inferred from neural time series. A popular statistical framework for inferring causal connectivity from observations is the directed probabilistic graphical modeling. Its common formulation is not suitable for neural time series since it was developed for variables with independent and identically distributed static samples. In this work, we propose to model and estimate the causal functional connectivity from neural time series using a novel approach that adapts directed probabilistic graphical modeling to the time series scenario. In particular, we develop the Time-Aware PC (TPC) algorithm for estimating the causal functional connectivity, which adapts the PC algorithm, a state-of-the-art method for statistical causal inference. We show that the model outcome of TPC has the properties of reflecting causality of neural interactions such as being non-parametric, exhibits the directed Markov property in a time-series setting, and is predictive of the consequence of counterfactual interventions on the time series. We demonstrate the utility of the methodology to obtain the causal functional connectome for several datasets including simulations, benchmark datasets, and recent multi-array electro-physiological recordings from the mouse visual cortex.

2. Front. Syst. Neurosci.

   Statistical Perspective on Functional and Causal Neural Connectomics: A Comparative Study

   Rahul Biswas and Eli Shlizerman

   Frontiers in Systems Neuroscience, 2022

   Abs DOI

   Representation of brain network interactions is fundamental to the translation of neural structure to brain function. As such, methodologies for mapping neural interactions into structural models, i.e., inference of functional connectome from neural recordings, are key for the study of brain networks. While multiple approaches have been proposed for functional connectomics based on statistical associations between neural activity, association does not necessarily incorporate causation. Additional approaches have been proposed to incorporate aspects of causality to turn functional connectomes into causal functional connectomes, however, these methodologies typically focus on specific aspects of causality. This warrants a systematic statistical framework for causal functional connectomics that defines the foundations of common aspects of causality. Such a framework can assist in contrasting existing approaches and to guide development of further causal methodologies. In this work, we develop such a statistical guide. In particular, we consolidate the notions of associations and representations of neural interaction, i.e., types of neural connectomics, and then describe causal modeling in the statistics literature. We particularly focus on the introduction of directed Markov graphical models as a framework through which we define the Directed Markov Property, an essential criterion for examining the causality of proposed functional connectomes. We demonstrate how based on these notions, a comparative study of several existing approaches for finding causal functional connectivity from neural activity can be conducted.

2020

1. Mach. Learn.

   On Some Graph-Based Two-Sample Tests for High Dimension, Low Sample Size Data

   Soham Sarkar, Rahul Biswas, and Anil K. Ghosh

   Machine Learning, 2020

   Abs DOI

   Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been proposed in the literature, which can be used for data of arbitrary dimensions. Most of these test statistics are computed using pairwise Euclidean distances among the observations. But, due to concentration of pairwise Euclidean distances, these tests have poor performance in many high-dimensional problems. Some of them can have powers even below the nominal level when the scale-difference between two distributions dominates the location-difference. To overcome these limitations, we introduce a new class of dissimilarity indices and use it to modify some popular graph-based tests. These modified tests use the distance concentration phenomenon to their advantage, and as a result, they outperform the corresponding tests based on the Euclidean distance in a wide variety of examples. We establish the high-dimensional consistency of these modified tests under fairly general conditions. Analyzing several simulated as well as real data sets, we demonstrate their usefulness in high dimension, low sample size situations.

2014

1. IEEE Trans. Sig. Proc.

   A Peak Synchronization Measure for Multiple Signals

   Rahul Biswas, Koulik Khamaru, and Kaushik Majumdar

   IEEE Transactions on Signal Processing, 2014

   Abs

   Peaks signify important events in a signal. In a pair of signals how peaks are occurring with mutual correspondence may offer us significant insights into the mutual interdependence between the two signals based on important events. In this work we proposed a novel synchronization measure between two signals, called peak synchronization, which measures the simultaneity of occurrence of peaks in the signals. We subsequently generalized it to more than two signals. We showed that our measure of synchronization is largely independent of the underlying parameter values. A time complexity analysis of the algorithm has also been presented. We applied the measure on intracranial EEG signals of epileptic patients and found that the enhanced synchronization during an epileptic seizure can be modeled better by the new peak synchronization measure than the classical amplitude correlation method.